Ticket to Ride is a board game created by Alan R. Moon that has been growing in popularity since its first release in 2004 by Days of Wonder. The game components include a map with cities and defined train routes, sets of 45 colored, plastic train car tokens for up to five players, destination tickets, and colored train cards. The premise of the game involves collecting enough of the colored train cards to claim or build train routes to connect various major cities in the United States and southern Canada to earn points as well as completing routes designated on the destination tickets. The game itself is not only a fun way to spend hours playing but it is also a good tool to showcase various concepts in graph theory and combinatorics. Graph theory may also be useful in creating or enhancing game play strategies.
Set Up and Game Play
The original version of the game has a map of the United States and southern Canada with 30 destination tickets. An expansion to the original game features larger sized card sets as well as 39 additional destination tickets for what is referred to as the “Mega Game” variant. Throughout this analysis, I will assume all features of the “Mega Game” will be used unless otherwise stated. Since the first release, maps of Europe, Switzerland, Germany, Scandinavia, Asia, India, Africa, and the Netherlands have been added as well as a card game, a dice expansion, and additional destination ticket expansions have been created with the same basic game play. The original map is shown in Figure 1.The set up for the game begins with each player selecting his/her set of color train tokens. Next each player is dealt four of the colored train cards that players can later use to build or purchase train routes...
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...the game. Other plays could be going for the same tickets and routes or they could be attempting to block other players from completing a strategy. Graph theory can be used to help but does little to account for these unknowns. Even without a winning strategy, Ticket to Ride is a good medium to showcase different definitions and theorems within graph theory in accessible terms that can be understandable to more people while still being an enjoyable game to play.
Works Cited
Days of Wonder, "Game Rules - Ticket to Ride." Last modified 2013. Accessed November 29, 2013. http://cdn0.daysofwonder.com/tickettoride/en/img/tt_rules_2013_en.pdf.
Harris, John M., Jeffry L. Hirst, and Michael J. Mossinghoff. Combinatorics and Graph Theory. New York: Springer, 2008.
Rosen, Kenneth H. Discrete Mathematics and Its Applications. New York: McGraw Hill Higher Education, 2007.
Since the beginning of the United States the American people have been on the move. Public transportation has played a major role in the development of this nation and in bringing its citizens together. In the book “Divided Highways”, author Tom Lewis takes the reader on a journey of the building of the Interstates and the consequences(good and bad) that came from them. Lewis believes that the Interstates are a physical characteristic of America and that it shows “all our glory and our meanness; all our vision and our shortsightedness”(xiv).
Amtrak is a state-owned, for profit, national railroad Company that provides efficient rail service both long and short distance transportation services. Being the primary provider of passenger-rail service in the U.S has a network that connects more than 500 cities and towns in 46 states. It offers long-distance and short-distance service corridors throughout nationwide operating daily, offering several choice of service class – first class sleeping car, custom class and economic services for different age groups with different travel needs. Amtrak receives federal funds to be used for their operating expenses. Its ridership and revenue growth have progressively increased in the past five-year successfully building relationships with the public and customers, recreating branding, and improving new services/quality, and it projects a continued growth in passenger revenue at about 4% per year with modest growth in passenger ridership (Exhibit C4.1, Page 245).
The Use of Setting in A Pair of Tickets and Everything that Rises Must Converge
The core cities of Minneapolis and St. Paul have stronger systems emerging in the Blue and Green Light Rail lines, however the southern suburb located Red BRT line is struggling with ridership. The proposed Orange BRT line to Burnsville will continue to have similar ridership problems if the transit engineers do not balance efficiency and speed to encourage riders to step out of their cars and onto the bus. Finally, without the extension of the Orange BRT line to Lakeville, the community will be restricted to the 467 Express Bus during rush hour, be forced to drive to at least Burnsville to other options, or continue to drive themselves and add to the
In today's day and age, an increasing urgency must be put on the issue of transportation and its relation to society. Man owes it to himself to address the issue of transportation with practicality and, as one of the biggest polluters, ultimate discretion. One of the most practical and responsible forms of transportation available today is mass transit. However, a problem is present in American society in that mass transit is not as plentiful as it should be. Societies' across the globe are embracing mass transit much more quickly than Americans are. This problem can be remedied through proper education of the benefits of mass transit. Mass transit is the ideal future of travel for several reasons. Of note: “mass transit costs less to the community, needs less urban space, is less energy-intensive, pollutes less, is the safest mode, improves accessibility to jobs, and offers mobility for all” (1). Mass transit is also a highly flexible mode of transportation, with many different methods of travel available. Of note for these: metros, buses, carpooling, light rail, and waterborne transports. Proponents of mass transit claim it will find solutions to problems concerning the economy, the environment, and the energy crisis, as well as improving overall quality of life (2). Each of these ideas will be examined more in-depth.
The entire lot is packed to the brim and the streets lined with cars. All of the giant machines are glistening in the distance. Gaining ground brings the echoing of earsplitting, fear induced screams to the ear. As the entrance becomes visible a particular smell arises, that brings back wonderful memories. The carnival is always engulfed in the wonderful aroma of sizzling deep fried batter sprinkled with a sweet, snow like versions of sugar. Once a whiff of the succulent concoction known as a funnel cake has been inhaled the visibility of excitement begins to pour out and aura of anticipation start to become heavy. Walking through the gates into lights that begin to blind but they do so elegantly with a sparkling of all colors of the rainbow. After the eyes adjust it is time for a plan to be made. The questions that need to be addressed are: Where to go first? What to ride? So many choices make it insanely hard to decide so a gut decision is the only
Stradling, S., Carreno, M., Rye, T., & Noble, A. (2007). Passenger perceptions and the ideal urban bus journey experience. Transport Policy, 14(4), 283-292. doi:10.1016/j.tranpol.2007.02.003
Often, when people think of the functions of train, they simply view them as modes of transport. But, in literature, this does not appear to be the case, as trains can be used to create a means of escapism for the characters
Flashing orange text on the black screen of the overhead time chart is a reminder that my ride will arrive in precisely three minutes. The white letters on the train stop sign read "Neureut Kirchfeld", reminding me once more of where I am. I am an exchange student in Karlsruhe, a German city of over 300,000 residents. It is early July and I am on my way to school. My normal is about three thousand miles away, but my peace of mind and happiness are right in front of me in the form of yellow street cars zooming by, storks gliding through the milky blue sky, and the slow breeze of a summer morning.
transportation role as the entryway to the Hogwarts express: the first step into the wizarding
Galley, Catherine C., and Briavel Holcomb. "Amusement Parks." St. James Encyclopedia of Popular Culture. Ed. Thomas Riggs. 2nd ed. Vol. 1. Detroit: St. James Press, 2013. 91-93. Gale Virtual Reference Library. Web. 27 Mar. 2014.
0.1 abstract In a graph theory the shortest path problem is nding a minimum path and distance between two vertices. The ap- plication in many areas of shortest path algorithms are such as geographical rout- ing, transportation, computer vision and VLSI design involve solving optimiza- tion problems on large planar graphs. To calculate the shortest path we need to know some algorithms like Kruskal's algorithm,Prim's algorithm,Dijkstra's algorithm,BellmanFord's algorithm.
Who doesn’t love a train ride? It offers a unique experience that no other vehicle can match. In a previous issue, we covered the Trans-Siberian Railway. In this article, we will be going on a journey aboard the Bernina Express, beginning our journey from Chur in Switzerland, traveling through wild Canton of Graubünden to Mediterranean Tirano in Italy.
This report illustrates the results and discussion of the Travelling Salesperson Problem (TSP). The travelling Salesperson travels from University Of Pretoria (UP) and has to travel to four possible locations using the shortest path. BFS and DFS will be used and compared according to efficiency of each for the Salesperson to reach his goal in the most optimal manner. The goal-state allows the Salesperson to visit all of the locations below and return to UP with the most optimal path. The following locations have to be visited:
It is considered a holistic approach that might be involved some factors providing an overall speed of journey (Mannering, Walter, and Scott, 2004). Wyatt (1997) states that the rail transportation has been made the urban areas to develop the transport network places with producing a good network to be placed over location with a poor network. For example in European Union (EU), the rail company had been employing around 570,000 people across passenger and freight operations in year 2012. From here, the rail transport is critical by the EU strategy to improve their economic condition. This rail sector had been makes a large contribution in oversea country.